Mobility Edge for the Anderson Model on the Bethe Lattice
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866910870471180288 |
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| author | Aggarwal, Amol Lopatto, Patrick |
| author_facet | Aggarwal, Amol Lopatto, Patrick |
| contents | We pinpoint the spectral decomposition for the Anderson tight-binding model with an unbounded random potential on the Bethe lattice of sufficiently large degree. We prove that there exist a finite number of mobility edges separating intervals of pure-point spectrum from intervals of absolutely continuous spectrum, confirming a prediction of Abou-Chacra, Thouless, and Anderson. A central component of our proof is a monotonicity result for the leading eigenvalue of a certain transfer operator, which governs the decay rate of fractional moments for the tight-binding model's off-diagonal resolvent entries. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_08949 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mobility Edge for the Anderson Model on the Bethe Lattice Aggarwal, Amol Lopatto, Patrick Probability Mathematical Physics Functional Analysis We pinpoint the spectral decomposition for the Anderson tight-binding model with an unbounded random potential on the Bethe lattice of sufficiently large degree. We prove that there exist a finite number of mobility edges separating intervals of pure-point spectrum from intervals of absolutely continuous spectrum, confirming a prediction of Abou-Chacra, Thouless, and Anderson. A central component of our proof is a monotonicity result for the leading eigenvalue of a certain transfer operator, which governs the decay rate of fractional moments for the tight-binding model's off-diagonal resolvent entries. |
| title | Mobility Edge for the Anderson Model on the Bethe Lattice |
| topic | Probability Mathematical Physics Functional Analysis |
| url | https://arxiv.org/abs/2503.08949 |